Adding and Subtracting Negative Integers as TemperaturesDate: 01/08/2004 at 00:52:50 From: Jonah Subject: word problems with negative integers If it's -20 degrees outside and it decreases 3 degrees what temperature is it? I know the answer is -23 degrees but it seems like it should be -17 degrees. When do you have to change the sign into addition? Date: 01/08/2004 at 12:13:38 From: Doctor Peterson Subject: Re: word problems with negative integers Hi, Jonah. It may help to look at an actual thermometer. It will look something like this: | + 40 | + 30 | + 20 | + 10 | ^ + 0 / \ | | + -10 | warmer (increasing temperature) | | + -20 ----+ | | + -30 | colder (decreasing temperature) | | + -40 \ / | V Suppose it was -20 degrees an hour ago, and now it has gone down 10 degrees. As it goes down, it will get farther away from 0 (since it is below zero to start with), so it will decrease from -20 degrees to -30 degrees! The number part (the 30, which is the "absolute value" of the temperature) increases because we are going away from zero while the temperature itself decreases (getting colder). If the temperature changed to -10, it would be warmer, not colder; that would be an increase in temperature. Does that make sense? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 01/08/2004 at 12:09:15 From: Doctor Rick Subject: Re: word problems with negative integers Hi, Jonah. It's easier to understand the correct answer if you look at a thermometer. If it had every degree labeled, portions of it would look like this: 5 | | 4 | | 3 | | 2 | | 1 | | 0 | | -1 | | -2 | | -3 | | -4 | | -5 | | -6 | | ......... -18 | | -19 | | -20 |-| * -21 | | | down 3 -22 | | V -23 | | * -24 | | -25 | | If you're at -20 and you go DOWN (decrease) 3 degrees, you get to -23. Now, to do it mathematically instead of looking at the thermometer, we do this: -20 - 3 which is the same as -20 + (-3) Subtracting is always the same as adding the opposite. Now, if you're familiar with the distributive property, we can remember that the negative sign means to multiply by -1, and we can do that multiplication just once: (-1*20) + (-1*3) = -1*(20 + 3) = -1*23 = -23 In other words, the rule for adding two negative numbers is to add the numbers without the negative signs, then make the result negative. If we wanted to INCREASE the temperature 3 degrees, we would do this: -20 + 3 I can again factor out a -1 like this: (-1*20) + (-1*-3) because 3 divided by -1 is -3. Then combine the -1's with the distributive property: -1(20 + -3) = -1(20 - 3) = -1*17 = -17 A rule to remember here is that if you are adding two numbers with DIFFERENT signs, you subtract the smaller from the bigger (ignoring the negative sign), and give the answer the sign of the bigger number. In this problem, -20 + 3, we look at 20 and 3, subtract 3 from 20 to get 17, then since the bigger number (20) has the negative sign, we make the answer negative: -17. I hope this helps you! - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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